EFFECT OF SURFACE WAVINESS ON BOUNDARY-LAYER-TRANSITION IN 2-DIMENSIONAL FLOW

In this paper, the effect of surface waviness on boundary-layer transi tion in two-dimensional subsonic how is investigated. The mean flow is calculated using an interacting boundary-layer procedure, thereby acc ounting for viscous-inviscid interaction. Then, the Linear parabolized stability equations are used to compute Tollmien-Schlichting-(TS) wav e amplification. As expected, wall waviness is found to destabilize TS waves. This effect is quantified by examining parameters such as wave height, wave length, wave number, wave location, unit Reynolds number , compressibility and pressure gradient and then comparing the results against those obtained in the absence-of waviness. From these results , an empirical equation is extracted which correlate the waviness size with the increment in the N-factor due to waviness. The present corre lation is compared with the empirical criteria derived from experiment s by Fage (Aeronautical Research Council, R & M 2120, 1943) and Carmic hael [Northrop Corp., Report No. NOR-59-438 (BLC-123), 1959]. In agree ment with the experiments, the present results show that the effect of waviness scales as h(2)/lambda where h is the wave height and lambda is the wavelength. Computational results indicated that the critical s ize of waviness below which waviness has no influence does not exist p rovided the waviness is located,in the unstable TS region. It is also shown that the centrifugal instability introduced by a wavy wall is re latively less significant and the dominant effect of waviness on bound ary-layer transition is through its effect on TS wave amplification. I t is likely, however, that streamwise vortices generated due to wavine ss will play a role in the nonlinear breakdown process. (C) 1998 Elsev ier Science Ltd. All rights reserved.